Note on Mean

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Arithmetic Means

Arithmetic Mean

If the total sum observation is divided by a total number of observations, then it is called arithmetic mean. It is denoted by \(\overline{X}\) (Read as X-bar)∴ Arithmetic Mean = \(\frac{Total\;sum\;of\;observation}{Total\;no.\;of\;observation}\)For example,Arithmetic mean of 1, 3, 7, 11, & 13

= \(\frac{1+3+7+11+13}{5}\)= \(\frac{35}{5}\)= 7

Calculation of Mean for individual seriesThe mean of individual series is calculated by adding all the observation and dividing the sum by the total number of observation.If x1, x2, x3, …………..xn are be n variants value of variable a. Then arithmetic mean is denoted by \(\overline{X}\) So, \(\overline{X}\) = \(\frac{x_1+ x_2+ x_3+ …………..x_n}{n}\) = \(\frac{∑X}{n}\)Where ∑X = sum of n observation or itemsn = no. of observations or itemsX = variable

Calculation of Mean for discrete seriesMean for discrete series can be calculated by\(\overline{X} = \frac{sum\;of\;the\;product\;of\;f\;and\;x}{sum\;of\;f}\)= \(\frac{∑fx}{N}\)

Calculation of Mean for continuous seriesFor calculating mean in continuous series the following formulae is used:\(\overline{X}\) = A + \(\frac{∑fx}{N}\) × i where, F = Frequency and A = mid-value